Heinrich von Weizsäcker

Regularization in Hilbert space under unbounded operators and general source conditions

The authors study ill-posed equations with unbounded operators in Hilbert space. This setup has important applications, but only a few theoretical studies are available. First, the question is addressed and answered whether every element satisfies some general source condition with respect to a given self-adjoint unbounded operator. This generalizes a previous result from Mathe and Hofmann (2008 Inverse Problems 24 015009). The analysis then proceeds to error bounds for regularization, emphasizing some specific points for regularization under unbounded operators. The study finally reviews two examples within the light of the present study, as these are fractional differentiation and some Cauchy problems for the Helmholtz equation, both studied previously and in more detail by U Tautenhahn and co-authors.

Identifying a Finite Graph by Its Random Walk

In this chapter, we illustrate by two examples and simplify the statement of the main result of a joint paper with Peter Scheffel [Scheffel and Weizsacker (1997)].